GDP PPP certainly doesn't get all the way, but it probably is more appropriate for this sort of comparison.

we have one, it's called MPS and it was used by the soviets and most of the communist countries including china until the 1990s. china has still not fully transitioned away from MPS and into SNA which is one reason their service sector share of GDP seems so impossibly low

Sounds like that could give useful insights. I couldn’t find MPS - do you have a link please?